Iterative Substructuring Method for Equilibrium Equations

Abstract

We consider some numerical solution method for the equilibrium equations. Algebraic problems of this form evolve from many applications such as structural optimization, fluid flow, and circuits. An approach, called the force method, to the solution to such problems involves dimension reduction nullspace schemes based upon computation of a basis for the nullspace for E. With emphasis on parallel computation, it is shown that the substructuring method is an efficient tool for nullspace computation. The purpose of this paper is to investigate the substructuring method for the solution step of the force method, and we suggest a mixed approach for solving equilibrium equations, consisting of both direct reduction in the substructures and the induced iterative algorithms to complete the computations.